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Yesterday, I asked a question about the square-cube law and propellant tanks.

I have a very similar question about Space Shuttle thermal protection system or TPS tiles. Does the mass ratio of TPS tiles improve in larger constructions? I mean, is the weight of the TPS divided by the mass of the whole construction better in larger ships, or do larger ships require thicker tiles, resulting in linear growth?

Starship, someday, will transport humans, so it will be much heavier when reentering the atmosphere (life support etc). Therefore, it will need to withstand much more heat. SpaceX doesn't have a different TPS design for these scenarios.

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    $\begingroup$ Do you have any source for a crewed Starship being much heavier? I would assume it would be much lighter since a lot of the cargo volume is occupied by air. Compare, for example, the mass of a fully loaded cargo Falcon 9 with Starlink with a crew launch to the ISS. Obviously, the mass of the first and second stage are the same, so the difference will be the mass of the payload fairings + the payload versus the mass of Crew Dragon plus cargo, consumables, and crew. Crew Dragon with everything inside is less than 7000kg, the Starlink satellites alone are more than 17000kg. $\endgroup$ Commented Oct 12, 2023 at 8:23
  • $\begingroup$ To be fair, that's not a 1:1 comparison since Crew Dragon goes to a higher-energy orbit and SpaceX reserves enough propellant for an RTLS landing. $\endgroup$ Commented Oct 12, 2023 at 8:24
  • $\begingroup$ @JörgWMittag During reentry, crewed starship will be heavier than the cargo starship due to additional equipment. cargo starship, on the other hand, will be empty during reentry $\endgroup$
    – Krzysiek
    Commented Oct 12, 2023 at 10:35

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The thermal protection system converts the kinetic energy of the spacecraft into heat during reentry. The total amount of heat that must be converted is a function of the spacecraft's mass.

The surface area, tile thickness, reentry time, and many other design parameters are engineered for a given spacecraft to arrive at the minimal mass TPS that will get the job done. For example, The Space Shuttle's thermal protection system used a range of tile thicknesses and a variety of different materials. According to this source, "The thickness of the tile is determined by the amount of heat the tile encounters."

If we assume that the surface area and thickness of the tiles are optimized for two different spacecraft, let's call them "Spacecraft A" and "Spacecraft B", and the mass of Spacecraft B is 2X the mass of Spacecraft A, the mass of the thermal protection system on Spacecraft B will also be 2X the mass of the thermal protection system on Spacecraft A.

While a larger spacecraft may be able to eke out some subtle performance gains for its thermal protection system, fundamentally the square-cube law doesn't apply to heat shield tiles.

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